Suppose that the weather in a certain city is either sunny, cloudy, or rainy on a given day, and consider the following:1) If it is sunny today there is a 70% chance it will be sunny tomorrow and a 30% chance that it will be cloudy.2) If it is cloudy today there is a 40% chance it will be sunny tomorrow, a 40% chance that it will be cloudy, and a 20% chance that it will be rainy.3) If it is rainy today there is a 40% chance it will be sunny tomorrow,30% chance that it will be cloudy, and a 30% chance that it will be rainy.Suppose the predicted weather for Friday is 55% sunny, 30% cloudy, and 15% rainy. What are the chances that Sunday will be rainy? Give your answer as a percentage and enter itinto Ans. Do not approximate. Do not include the % symbol.

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Answered: Suppose that the weather in a certain…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Example 2.3.14 Three boxes having the same appearance have the folloW- ing proportions of white and black balls-Box I: 1 white and 2 black; Box II: 2 white and 1 black; box III: 2 white and 2 black. One of these boxes is selected at random, and one ball is drawn randomly from it. It turns out to be white. What is the probability that the third box will be chosen.
Question 5 A certain brand of pregnancy test will be positive for a pregnant woman 84% of the time. It correctly returns a negative test in 79% of woman that are not pregnant. Given that one in five woman who take the test are actually pregnant, draw a tree diagram to represent this information and find the probability that a woman who uses the test is pregnant and tests positive. Find also the probability of a false positive and, hence, comment on the reliability of the test.
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2- A driver has three ways to get from one city to another. There is (80%) probability of encountering a traffic jam on route (1), a (60%) probability on route (2) and a (30%) probability on route (3). Because of other factors, such as distance and speed limits, the driver uses route 1 (50%) of the time and route 2 and route 3 each (25%) of the time. If the driver call the dispatcher to inform him that she is in a traffic jam, find the probability that she has selected route 1. 3
2. There are two boxes. Box A has 3 white chips and 1 red chip, Box B has 2 white chips and 1 red chip. There is a 40% chance that Box A will be the first box selected (that is, there is a 60% chance that Box B will be selected first.) A box is chosen at random. From the first box chosen, a chip is selected at random, the color is observed, and then the chip is placed in the other box (the one not chosen first). A chip is then selected at random from the other box and the color is observed. a. C. Find the probability of observing 2 red chips in a row. b. Find the probability of observing a white chip from the other box (the last box chosen). Given that one observes a white chip from the other box, find the probability that Box A was the first box chosen.
Solved question 36
Assume that the fleet consists of 30 percent Lexus, 30 percent Infinity, and 40 percent automobiles. 80 percent of the Lexus cars, 60 percent of the Infinities, and 70 percent Mercedes have CD players. Use this information to answer the following questions. (1) What is the probability that a randomly selected car has a CD player? (2) What is the probability that a randomly selected car either is a Mercedes or has a CD pl.
22. The astrology software package Java Kimset is designed to help day traders choose stocks based on the position of the planets and constellations. When Benjamin ran it yesterday, it informed him that there was a .5 probability that Amazon.com will go up this afternoon, a .2 probability that Yahoo.com will go up this afternoon, and a .2 chance that both will go up this afternoon. What is the probability that either Amazon.com or Yahoo.com will go up this afternoon?
Example 2.3.13 Two urns contain 3 white, 7 red, 15 black, and 10 white, 6 red, 9 black balls respectively. One ball is drawn from each urn. Find the probability that both the balls are of the same colour.
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1. Why is it so much more likely that some pair of people at a party will have the same birthday, than that someone at the party will have a birthday today?
18) Mordor is considering invading and conquering Gondor. Gondor has an alliance with Rohan, however it is unclear whether or not Rohan will maintain the alliance. Assume that there is a 30% probability that Rohan is a loyal ally that would help Gondor, and a 70% probability that they would abandon Gondor. Neither Gondor nor Mordor know whether Rohan is a loyal ally, although of course Rohan knows their own type. After nature chooses whether Rohan is a loyal ally, Gondor can either surrender or not. If Gondor surrenders, the game ends. If Gondor does not surrender, Mordor can invade or not. If Mordor does not invade, the game ends. If Mordor does invade, Rohan can either ride to Gondor's aid or not. If Rohan aids Gondor, the alliance will prevail. If they do not, Mordor will prevail. Gondor gets -80 utility for surrendering, -100 utility from being conquered, and 30 utility for winning the war, and 70 utility if Mordor does not invade. Mordor gets 100 utility if Gondor surrenders, 50…

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